The momentum that carried Rick Santorum to a photo finish with Mitt Romney in Tuesday’s Iowa caucuses should help him battle for the Republican presidential nomination in New Hampshire and beyond, supporters contend.

But some political strategists are skeptical. By concentrating so much on Iowa, Santorum ran what was essentially a governor’s race, they said. And he will most likely face the same post-Iowa challenges that wiped out former Arkansas Gov. Mike Huckabee after he won the Iowa GOP caucuses in 2008.

Republican strategist David Polyansky, who worked for Huckabee in 2008 and for U.S. Rep. Michele Bachmann until September, remarked, “It would be an upset of epic proportions to carry momentum from Iowa and turn it into a nomination.”

Some of the issues Santorum faces include raising money for expensive TV advertising campaigns, getting on ballots and establishing a national organization.

Santorum, who finished second in the Iowa caucuses, just eight votes behind Romney, told reporters in Iowa this week that he remained optimistic about his chances in other states. However, he’s been stuck in single digits in the polls in New Hampshire, which has a Republican primary next week.

Romney is heavily favored in that race. But Santorum is hopeful of finishing in the upper tier of Republican candidates, which he believes will help him in South Carolina’s early primary. His message of fiscal conservatism and traditional family values “is a solid one for every state in the country,” he said.

Cody Brown, Santorum’s Iowa campaign director, said Wednesday that his candidate already had campaign organizations in place in New Hampshire, where 23 state legislators have endorsed him, and in South Carolina, where he has 100 county campaign captains.

“For a lot of these campaigns, it is about putting infrastructure in place to track who is supporting you, why they are supporting you,” and how those who support other candidates might be peeled away, Brown said. “If you have those databases in place that is half the battle right there.”

Iowa Secretary of State Matt Schultz, who endorsed Santorum in December, said he thought the former Pennsylvania senator has a chance as a national candidate, adding that his Iowa momentum should be a boon for fundraising.

Anyone who heard Santorum’s post-caucuses speech on Tuesday night would be impressed, Schultz said. Santorum told the story of how his grandfather had immigrated from Italy to work in Pennsylvania’s coal mines and how he had sacrificed to bring his family to America.

“That speech really resonates with Americans,” Schultz said. “I have heard him give it many times, but the way he sequenced the elements was brilliant.”

The Santorum campaign’s Iowa headquarters in Urbandale will remain open for now, Brown said. Campaign officials will consider the option of using the office and its phone bank to conduct campaign work outside Iowa, he said. “Just because we have a campaign in New Hampshire doesn’t mean everybody has to go to New Hampshire,” he said.

Register chief political reporter Jennifer Jacobs contributed to this story.